Help with: Venn Diagram/ Probability JC Math Question

lyndonjones

Ok so was helping my daughter with her 2nd years J.C. Math last night and I became bogged down with the following question...

In a survey of 45 University students they were asked which countries they visited during their summer holidays - England, France or Germany

No one had been to all three countries but 13 had been to England, 19 to France and thirteen to Germany. 13 had visited none of there countries. One had visited England and Germany only and four had visited England and France only

Question - Draw a Venn diagram to represent the above information

How many had been to at least one country?

How many had been to one country only?

Two countries?

Based on the information we can determine that 32 students visited a country [45 - 13] so probability of a student visiting one country is 32/45

Completing the Venn digram to answer the next questions has us bogged down. The total should add to 32 within the Venn circles.

There "seems" to be some information missing or I can decipher the clues therein!! Probably the latter!!!

We don't know how many, if any, visited Germany and France only.

Any help appreciated!!!

Sky King

Here's what I did:

(Disclaimer: I am NOT a mathematician or maths teacher and this could be, and in all probability IS incorrect... i am just bored here... so please don't accept my answer as correct.)

Based on the information you are given you can fill out the venn diagram as follows:




So from this you can deduce that since Germany = 13, 1+Z+Y=13 or Z+Y=12

Since 19 went to france 4+X+Y = 19 or X+Y = 15

Since 13 got no holiday there were 32 kids in total on holidays so 8+4+1+X+Y+Z = 32
=X+Y+Z = 19

Since X+ Y = 15 we can say that X = 15-Y and sub it into the green equation above

15-y+y+z=19
15+z=19
z=4

We know from the brown equation that Z+Y = 12 and we just found out that z=4 so this means y=8 and x= 7.

lyndonjones

Thanks for the detailed response.

Looks correct even though the answer her teacher gave her differs!!


TBH this solution is using simultaneous equations, if I am not mistaken, bit advanced for 2nd years, don't you think?

Glowworm4

I got the same answer as Sky King, but did it a slightly different way which might be easier to understand for a 2nd year.

Here it is:



(The brackets around certain numbers means that that is the total for that specific set, e.g. England [13] means that the total number of elements in the set England is 13)

My equation is as follows:

45 = 8 + 4 + 1 + (15 - x) + x + (12 - x) + 13
45 = 26 + 15 - x + x +12 - x
45 = 53 -x .................................................. (+x and -x cancel)
45 - 53 = -x
-8 = -x
8 = x ........................................................(change all signs)


Your answers will then be:

i) 8 + 4 + 1 + 4 + 7 + 8 = 32

ii) 4 + 8 + 7 = 19

iii) 8 + 1 + 4 = 13


I hope that this one might be easier for your daughter to understand and to use.

Sky King

lyndonjones wrote: »

bit advanced for 2nd years, don't you think?

I don't think, I am not a teacher or a student and I can't remember what I was doing in school and when. I thought simultaneous eqns were on the JC syllabus though... but anyway no matter.

Glad it's right anyway. Killed a good 25 mins in work for the this morning that did.:pac: